Direct sum of Lie algebras
= Direct sum of Lie algebras
The direct sum $\mathfrak g\oplus\mathfrak h$ has componentwise bracket
$$
[(x,y),(x',y')]=([x,x'],[y,y']).
$$
The two summands are commuting <ideal of a Lie algebra>[ideals].
= Direct sum of Lie algebras
The direct sum $\mathfrak g\oplus\mathfrak h$ has componentwise bracket
$$
[(x,y),(x',y')]=([x,x'],[y,y']).
$$
The two summands are commuting <ideal of a Lie algebra>[ideals].